Welcome department's first study being kept secret (6)
I believe the answer is:
hidden
'secret' is the definition.
(I know that secret can be written as hidden)
'welcome department's first study being kept' is the wordplay.
'welcome' becomes 'hi' (both are greetings).
'department's first' becomes 'd' (1st letter of 'department').
'study' becomes 'den' (term for a study or office).
'being kept' indicates putting letters inside.
'd' inserted within 'den' is 'dden'.
'hi'+'dden'='HIDDEN'
(Other definitions for hidden that I've seen before include "Concealed, kept secret" , "Obscure" , "Not accessible to view" , "Concealed, placed out of sight" , "Covert, obscured" .)